Reconstruction of the initial condition in parabolic equations with Log-Lipschitz coefficients

Abstract

We consider a parabolic equation whose coefficients are Log-Lipschitz continuous in $t$ and Lipschitz continuous in $x$. Combining a recent conditional stability result with a well posed variational problem, we reconstruct the initial condition of an unknown solution from a rough measurement at the final time.

11 pages; this version of the article has been accepted for publication in Annali di Matematica Pura e Applicata

References in corpus (1)

• Conditional stability up to the final time for backward-parabolic equations with Log-Lipschitz coefficients